Semiclassical standing waves with clustering peaks for nonlinear schrodinger equations / [electronic resource] Jaeyoung Byeon, Kazunaga Tanaka.

By: Byeon, Jaeyoung, 1966-Contributor(s): Tanaka, Kazunaga, 1959-Material type: TextTextSeries: Memoirs of the American Mathematical Society ; v. 1076Publisher: Providence, Rhode Island : American Mathematical Society, 2014Description: 1 online resource (pages cm.)Content type: text Media type: unmediated Carrier type: volumeISBN: 9781470415303 (online)Subject(s): Gross-Pitaevskii equations | Schr�odinger equation | Standing waves | Cluster analysisAdditional physical formats: Semiclassical standing waves with clustering peaks for nonlinear schrodinger equations /DDC classification: 530.12/4 LOC classification: QC174.26.W28 | B94 2014Online resources: Contents | Contents
Contents:
Chapter 1. Introduction and results Chapter 2. Preliminaries Chapter 3. Local centers of mass Chapter 4. Neighborhood $\Omega _\varepsilon (\rho ,R,\beta )$ and minimization for a tail of $u$ in $\Omega _\varepsilon $ Chapter 5. A gradient estimate for the energy functional Chapter 6. Translation flow associated to a gradient flow of $V(x)$ on ${\bf R}^N$ Chapter 7. Iteration procedure for the gradient flow and the translation flow Chapter 8. An $(N+1)\ell _0$-dimensional initial path and an intersection result Chapter 9. Completion of the proof of Theorem 1.3 Chapter 10. Proof of Proposition 8.3 Chapter 11. Proof of Lemma 6.1 Chapter 12. Generalization to a saddle point setting
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Includes bibliographical references.

Chapter 1. Introduction and results Chapter 2. Preliminaries Chapter 3. Local centers of mass Chapter 4. Neighborhood $\Omega _\varepsilon (\rho ,R,\beta )$ and minimization for a tail of $u$ in $\Omega _\varepsilon $ Chapter 5. A gradient estimate for the energy functional Chapter 6. Translation flow associated to a gradient flow of $V(x)$ on ${\bf R}^N$ Chapter 7. Iteration procedure for the gradient flow and the translation flow Chapter 8. An $(N+1)\ell _0$-dimensional initial path and an intersection result Chapter 9. Completion of the proof of Theorem 1.3 Chapter 10. Proof of Proposition 8.3 Chapter 11. Proof of Lemma 6.1 Chapter 12. Generalization to a saddle point setting

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Electronic reproduction. Providence, Rhode Island : American Mathematical Society. 2014

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